A line cuts two sides `AB` and `AC` of `DeltaABC` at points `P` and `Q` respectively. Prove `(A(DeltaAPQ))/(A(DeltaABC))=(APxxAQ)/(ABxxAC)`.

A circle with centre P is inscribed in the Delta ABC Side AB, side BC and side A C touch the circle at points L,M and N respectively . Prove that : A (DeltaABC ) = 1/2 (AB +BC + AC) xxr

The vertices of a DeltaABC are A(3, 0), B (0, 6) and C (6, 9) . A straight line DE divides AB and AC in the ration 1:2 at D and E respectively, prove that (DeltaABC)/(DeltaADE) = 9

A circle touches the side BC of DeltaABC at P and touches AB and AC produced at Q and R respectively. Prove that AQ=1/2(Perimeter of DeltaABC).

Mid-points of the sides AB and AC of a DeltaABC are (3, 5) and (-3, -3) respectively, then the length of the side BC is

In the given figure, the sides AB and AC of DeltaABC have been extended to D and E respectively. If xgty , show that ABgtAC .

Line m intersects sides AB and AC of DeltaABC in the points P and Q respectively. AP=4.2, PB=6.3, AQ=4, QC=6 . State with reason whether line m is parallel to side BC or not.

CD and GH are respectively the bisectors of angleACB and angleEGF such that D and H lie on sides AB and FE of DeltaABC and DeltaEFG respectively. If DeltaABC ~ DeltaFEG show that : (CD)/(GH) = (AC)/(FG)